Dr Niall Madden

BSc, MSc, PhD

Contact Details

Lecturer Above The Bar
------------------------
ADB-1013
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics

T: 091-493803
E: Niall.Madden@NUIGalway.ie
W: http://www.maths.nuigalway.ie/~niall
 
researcher

Biography

BSc (Mathematics and Computing) UCG, 1994
MSc (Mathematics) UCC, 1996
PhD (Mathematics) NUI Cork, 2000


Since 2000 I am a lecturer in Mathematics at NUI Galway. My main research interests are concerned the analysis of numerical schemes for differential equations. I am particularly involved in the solution of singularly perturbed differential equations, by finite element and finite difference methods, and in the application of novel methods in numerical modelling.

Research Interests

Numerical analysis of singularly perturbed differential equations. Finite element and finite difference methods. Layer resolving meshes. Numerical linear algebra.

Research Projects

  Project Start Date End Date
IRCSET EMBARK POSTGRAD MULTIGRID METHODS FOR SINGULARLY PERTURBED PROBLEMS (ANH THAI NHAN) RS/2011/179 NIALL MADDEN 01-SEP-11 31-AUG-15
SFI RFP NUMERICAL MODELLING OF ADVECTION-DIFFUSION 01-SEP-08 01-NOV-12
IRCSET EMBARK 04 MEGHAN STEPHENS MADDEN 01-SEP-04 30-APR-09
MF2005 FAST PARALLEL SOLVERS N MADDEN 01-NOV-05 19-JUN-09
MF2003 MF 89 03 M NIALL MADDEN 01-JAN-04 28-FEB-07

Peer Reviewed Journals

  Year Publication
(2016) 'An optimal time-stepping algorithm for unsteady advection-diffusion problems'
Chadha, NM,Madden, N (2016) 'An optimal time-stepping algorithm for unsteady advection-diffusion problems'. Journal Of Computational And Applied Mathematics, 294 :57-77 [DOI] [Details]
(2015) 'A multiscale sparse grid finite element method for a two-dimensional singularly perturbed reaction-diffusion problem'
Madden, N,Russell, S (2015) 'A multiscale sparse grid finite element method for a two-dimensional singularly perturbed reaction-diffusion problem'. Advances In Computational Mathematics, 41 :987-1014 [DOI] [Details]
(2013) 'Robust solution of singularly perturbed problems using multigrid methods'
MacLachlan, Scott and Madden, Niall (2013) 'Robust solution of singularly perturbed problems using multigrid methods'. SIAM J. Sci. Comput, 35 (5):2225-2254 [DOI] [Details]
(2013) 'Bayesian networks for mathematical models: Techniques for automatic construction and efficient inference'
Enright, CG,Madden, MG,Madden, N (2013) 'Bayesian networks for mathematical models: Techniques for automatic construction and efficient inference'. International Journal Of Approximate Reasoning, 54 :323-342 [DOI] [Details]
(2013) 'hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems'
Xenophontos, Christos; Melenk, Markus; Madden, Niall; Oberbroeckling, Lisa; Panaseti, Pandelitsa; Zouvan; Antri . (2013) 'hp Finite Element Methods for Fourth Order Singularly Perturbed Boundary Value Problems'. Lecture Notes In Computer Science, 8236 :532-539 [DOI] [Details]
(2012) 'John Todd and the development of modern numerical analysis'
Niall Madden (2012) 'John Todd and the development of modern numerical analysis'. Bulletin Of The Irish Mathematical Society, 69 (Summer):11-23 [ARAN Link] [Details]
(2011) 'A two-weight scheme for a time-dependent advection-diffusion problem'
Naresh M. Chadha and Niall Madden (2011) 'A two-weight scheme for a time-dependent advection-diffusion problem'. Lecture Notes In Computational Science And Engineering, 85 :99-108 [DOI] [ARAN Link] [Details]
(2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source'
Niall Madden and Kajal Kumar Mondal (2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source'. Lecture Notes In Computational Science And Engineering, 81 :177-185 [ARAN Link] [Details]
(2010) 'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS'
Linss, T,Madden, N (2010) 'ANALYSIS OF AN ALTERNATING DIRECTION METHOD APPLIED TO SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS'. International Journal Of Numerical Analysis And Modeling, 7 :507-519 [Details]
(2009) 'A Parameter-Uniform Schwarz Method for a Coupled System of Reaction Diffusion Equations'
Stephens, M., Madden, N. (2009) 'A Parameter-Uniform Schwarz Method for a Coupled System of Reaction Diffusion Equations'. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 230 (2):360-370 [DOI] [Details]
(2009) 'A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions'
Liu, F,Madden, N,Stynes, M,Zhou, AH (2009) 'A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions'. Ima Journal Of Numerical Analysis, 29 :986-1007 [DOI] [Details]
(2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters'
Stephens, M., Madden, N. (2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters'. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING, 69 :247-255 [Details]
(2009) 'Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems'
Linss, T,Madden, N (2009) 'Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems'. Ima Journal Of Numerical Analysis, 29 :109-125 [DOI] [Details]
(2008) 'A parameter-robust numerical method for a system of reaction-diffusion equations in two dimensions'
Kellogg, RB,Madden, N,Stynes, M (2008) 'A parameter-robust numerical method for a system of reaction-diffusion equations in two dimensions'. Numerical Methods For Partial Differential Equations, 24 :312-334 [DOI] [Details]
(2007) 'Parameter uniform approximations for time-dependent reaction-diffusion problems'
Linss, T,Madden, N (2007) 'Parameter uniform approximations for time-dependent reaction-diffusion problems'. Numerical Methods For Partial Differential Equations, 23 :1290-1300 [DOI] [Details]
(2007) 'Software for calculating blood lactate endurance markers'
Newell, J ; Higgins, D; Madden, N; Cruickshank, J; Einbeck, J; McMillan, K; McDonald, R (2007) 'Software for calculating blood lactate endurance markers'. Journal Of Sports Sciences, [Details]
(2005) 'Grid equidistribution for reaction-diffusion problems in one dimension'
Kopteva, N,Madden, N,Stynes, M (2005) 'Grid equidistribution for reaction-diffusion problems in one dimension'. Numerical Algorithms, 40 :305-322 [DOI] [Details]
(2004) 'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations'
Linss, T,Madden, N (2004) 'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations'. Computing, 73 :121-133 [DOI] [Details]
(2004) 'A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations'
Linss, T,Madden, N (2004) 'A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations'. Applied Mathematics And Computation, 148 :869-880 [DOI] [Details]
(2003) 'An improved error estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'
Linss, Torsten and Madden, Niall (2003) 'An improved error estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'. Comput. Methods Appl. Math, 3 (3):417-423 [DOI] [Details]
(2003) 'An improved estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'
Linss, T., Madden, N. (2003) 'An improved estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 3 (3):417-423 [Details]
(2003) 'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems'
Madden, N,Stynes, M (2003) 'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems'. Ima Journal Of Numerical Analysis, 23 :627-644 [Details]
(1997) 'Efficient generation of oriented meshes for solving convection-diffusion problems'
Madden, N,Stynes, M (1997) 'Efficient generation of oriented meshes for solving convection-diffusion problems'. International Journal For Numerical Methods In Engineering, 40 :565-576 [Details]
(1996) 'Linear enhancements of the streamline diffusion method for convection-diffusion problems'
Madden, N,Stynes, M (1996) 'Linear enhancements of the streamline diffusion method for convection-diffusion problems'. Computers & Mathematics With Applications, 32 :29-42 [Details]

Book Chapters

  Year Publication
(2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source'
Madden, Niall and Mondal, Kajal Kumar (2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source' In: Springer, Heidelberg. [Details]
(2011) 'A two-weight scheme for a time-dependent advection-diffusion problem'
Chadha, Naresh M. and Madden, Niall (2011) 'A two-weight scheme for a time-dependent advection-diffusion problem' In: Springer, Heidelberg. [Details]
(2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters'
Stephens, Meghan and Madden, Niall (2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters' In: Springer, Berlin. [Details]

Conference Publications

  Year Publication
(2012) APPLICATIONS OF MATHEMATICS 2012
Niall Madden and Martin Stynes (2012) A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems . In: J. Brandts, J. Chleboun, S. Korotov, K. Segeth, J. Šístek & T. Vejchodský eds. APPLICATIONS OF MATHEMATICS 2012 Prague, , 02-MAY-12 - 05-MAY-12 , pp.188-196 [Details]
(2011) Proc. 13th Conference on Artificial Intelligence in Medicine
Catherine G. Enright, Michael G. Madden, Niall Madden, and John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs Proc. 13th Conference on Artificial Intelligence in Medicine Slovenia, [Details]
(2011) AIME
Catherine G. Enright and Michael G. Madden and Niall Madden and John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs . In: Mor Peleg and Nada Lavrac and Carlo Combi eds. AIME , pp.159-168 [Details]
(2010) Proceedings of BIOSIGNALS-2010, Part of the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies
Catherine G. Enright & Michael G. Madden (NUI Galway), Stuart J. Russell & Norm Aleks (UC Berkeley), Geoffrey Manley (UCSF), John Laffey (NUI Galway), Brian Harte & Anne Mulvey (University Hospital Galway), Niall Madden (NUI Galway) (2010) Modelling Glycaemia in ICU Patients: A Dynamic Bayesian Network Approach Proceedings of BIOSIGNALS-2010, Part of the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies Valencia, Spain, [Details]

Edited Books

  Year Publication
(2003) The Second Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2002).
Sharon Flynn, Ted Hurley, Micheal Mac an Airchinnigh, Niall Madden, Michael McGettrick, Michel Schellekens and Anthony Seda (Ed.). (2003) The Second Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2002). x: Electronic Notes in Theoretical Computer Science (Elsevier). [DOI] [Details]

Conference Paper

  Year Publication
(2006) A parameter-robust numerical method for a coupled system of two dimensional reaction-diffusion equations. 4th Conference on Finite Difference Methods: Theory and Applications.
Madden, N., Bruce, R., Kellogg, B., Stynes, M. (2006) A parameter-robust numerical method for a coupled system of two dimensional reaction-diffusion equations. 4th Conference on Finite Difference Methods: Theory and Applications. Lozenetz, Bulgaria: Conference Paper [Details]
(2005) Model free endurance markers based on the second derivative of blood lactate curves. 20TH IWSM, STATISTICAL SOLUTIONS TO MODERN PROBLEMS.
Newell, J., Einbeck, J., Madden, N., McMillan, K. (2005) Model free endurance markers based on the second derivative of blood lactate curves. 20TH IWSM, STATISTICAL SOLUTIONS TO MODERN PROBLEMS. Swiss-Grand Resort & Spa on Bondi Beach in Sydney: Conference Paper [Details]
(2004) On the application of robust numerical methods to a complete flow wave-current model. Boundary and Interior Layers ONERA.
Niall Madden, Martin Stynes, and Gareth Thomas (2004) On the application of robust numerical methods to a complete flow wave-current model. Boundary and Interior Layers ONERA. Conference Paper [ARAN Link] [Details]
(2004) On equidistribution for reaction-diffusion problems. Workshop on problems with boundary-layer phenomena.
Kopteva, N., Madden, N., Stynes, M. (2004) On equidistribution for reaction-diffusion problems. Workshop on problems with boundary-layer phenomena. University of Limerick: Conference Paper [Details]

Unpublished work

  Year Publication
(2012) Robust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensions.
MacLachlan, Scott; Madden, Niall (2012) Robust solution of singularly perturbed problems using multigrid methods: analysis and results in one and two dimensions. Unpublished work [ARAN Link] [Details]

Professional Associations

  Association Function From / To
IMS: Irish Mathematical Society 01-SEP-00 /
SIAM: Society for Industrial and Applied Mathematics 01-APR-00 /

Education

  Year Institution Qualification Subject
2000 National University of Ireland, Cork PhD Mathematics
1996 University College Cork Msc Mathematics
1994 University College Galway BSc Computing Studies and Mathematical Science

Other Activities

  Description

Director of the NUI Galway Bachelor Of Science: Computer Science programme.

Member of the Society for Industrial and Applied Mathematics (SIAM): UK and Republic of Ireland Section

Member of the Irish Mathematical Society

Academic Director of Modular Programme in Science and Technology Studies

Teaching Interests

Mathematics, particularly applications of computer methods and development of algorithms.

In the academic year 2014/2014 I am teaching the following modules.
Semester 1

 Semester 2
  • CS319: Scientific Computing
  • MA385/MA531: Numerical Linear Algebra